1. Field of the Invention
The invention relates to a method of seismic data enhancement to suppress noise.
2. Description of the Prior Art
In seismic exploration a signal is provided at or in the vicinity of the earth's surface. Part of the signal penetrates into the subsurface and is reflected at the interfaces of geological formations linked with changes in the elastic properties. With the aid of a plurality of receivers, these reflected signals are recorded at the surface in the form of analog signals or as series of digital values called traces. The total number of simultaneously recorded traces is termed a seismogram. These receivers record not only earth vibrations generated by the reflections of the emitted seismic signal, hereinafter called the desired signal, but also incidental earth vibrations. Earth vibrations not related to the emitted signal as, for example, caused by traffic, machines or by the swaying of trees in the wind whose motion is transferred by the roots to the earth, are called uncorrelated noise. This also applies to the noise generated by ships in off-shore seismic. In addition, waves occur in connection with the emitted signal, such as surface waves or the airwave which, however, are not regarded as the desired signal but as organized noise.
In order to reduce the noise in the recorded seismogram whose energy can exceed that of the reflected desired signal when using the conventional surface sources of seismic energy, it is usual to emit several signals in succession and to add the individual elementary seismograms obtained with these signals to form a final seismogram (vertical stacking). In order, furthermore, to attenuate the organized noise, the individual seismic signals are emitted from different points which are set not too far apart. As a consequence, surface-coupled, correlated noise trains are attenuated to a greater degree than the recorded desired signals coming from deep interfaces.
So-called horizontal stacking performed in the further course of processing seismic data is based on the same principle. In horizontal stacking all traces containing reflected signals from identical subsurface points are combined to form one trace. Differences in the propagation time of the signals are compensated for prior to stacking by so-called static and dynamic corrections.
This kind of noise suppression is only optimal if the amplitudes of the noise are normally distributed on all traces, have the same variance on all traces and are completely uncorrelated. The last condition means not only--as presupposed in the following--that no connection exists between the noise on difference traces, but also that on each trace of a seismogram, the amplitude of the noise at a certain time is completely independent from the amplitudes of the noise at other times.
In an improved method (U.S. Pat. No. 3,398,396) called diversity stack, the traces are divided into individual sections. In each section the total amount of energy of the desired signal and of the noise is determined and allocated to the middle of the interval. When adding the individual seismograms the values of these traces are multiplied by factors which are determined by interpolation from the reciprocal values of the total energy allocated to the centres of the two neighboring sections. This method is advantageous if the amplitudes of the noise are normally distributed and uncorrelated.
Further methods for the suppression of noise by weighted vertical stacking are described, for example, in the U.S. Pat. No. 3,622,967 (Foster et al) and the Canadian Pat. Nos. 904,971 (George et al) and 932,443 (Diltz et al). In these three publications, different methods are used to determine weight factors with the aid of which traces with a higher proportion of noise are taken into less account in the addition than traces with less noise.
These methods of noise suppression are not optimal, particularly when the noise is not distributed completely at random but has a certain structure. This is, for example, the case when not all frequencies occur to the same extent in the noise but some frequencies of narrow frequency bands are particularly strongly represented and expresses itself, for example, in that the autocovariance function of the noise has not only main maximum but also pronouned secondary maxima. In this case it is possible to use the noise received over a certain period of time to deduce the noise earlier or later times. The noise is to a certain extent--at least for short periods of time--predictable. Expressed differently this means that the probability for the occurrence of a certain noise amplitude is not independent of the noise amplitudes at earlier or later times.
The present invention is a method for suppressing noise in seismic data which are provided with the aid of energy sources capable of radiating reproducible signals into the subsurface and which are recorded by at least one receiver or one receiver group whose position does not change at all or only slightly, in the form of an analog signal, or a series of digital numerical values, the totality of the elementary traces recorded when a signal is radiated from the receiver/receivers or receiver groups being termed an elementary seismogram and the elementary seismograms being combined to form a final seismogram to improve the ratio of desired signal to noise, and said method also being provided for suppressing noise trains in seismic data with different transmitting and recording points but a common point of reflection, said method characterized in that these elementary seismograms are all brought into that form which they would have if they had all been provided by the same signal; that by combination of at least two elementary seismograms, noise seismograms are formed which no longer contain the desired signal or in which the energy of the desired signal is negligible compared with that of the noise, the number of different noise seismograms being at least equal to the number of elementary seismograms to be combined to form a final seismogram; the probability distribution of the noise is determined for each trace of the noise seismogram; the probability distribution of the noise in the traces of the elementary seismograms is determined from the probability distributions of the noise in the traces of the noise seismograms; and in that the most probable form of the desired signals is determined from the probability distribution of the noise in the traces of the elementary seismograms.